Stability of abstract differential equations at constantly acting disturbances

Stability Properties of Differential Systems under Constantly Acting Perturbations

In this article, we find stability criteria for perturbed differential systems, in terms of two measures. Our main tool is a definition of total stability based on two classes of perturbations.

Stability of Nonlinear Systems under Constantly Acting Perturbations 273

Asymptotic Stability of Solutions to Abstract Differential Equations

An evolution problem for abstract differential equations is studied. The typical problem is: u̇ = A(t)u+F(t,u), t ≥ 0; u(0) = u0; u̇ = du dt (∗) Here A(t) is a linear bounded operator in a Hilbert spaceH, and F is a nonlinear operator, ‖F(t,u)‖≤ c0‖u‖, p > 1, c0, p = const > 0. It is assumed that Re(A(t)u,u) ≤ −γ(t)‖u‖2 ∀u ∈ H, where γ(t) > 0, and the case when limt→∞ γ(t) = 0 is also considered....

Total Stability in Abstract Functional Differential Equations with Infinite Delay

Recently, authors [2] have discussed some equivalent relations for ρ-uniform stabilities of a given equation and those of its limiting equations by using the skew product flow constructed by quasi-processes on a general metric space. In 1992, Murakami and Yoshizawa [6] pointed out that for functional differential equations with infinite delay on a fading memory space B = B((−∞, 0];R) ρ-stabilit...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty